City Council Speaker Christine Quinn is moving to rein in budget-busting contracts with outside firms after the high-profile CityTime scandal rocked the Bloomberg administration, The Post has learned.

Quinn, typically a close ally of the mayor, will testify at a council hearing this morning that she wants to regulate the administration’s use of expensive contracts with private companies to prevent runaway costs.

She will announce she is supporting a bill, sponsored by Councilwoman Letitia James (D-Brooklyn), to require that all city agencies report to the council when they approve large budget increases to any contracts of at least $1 million.

The legislation would mandate the agencies notify the council if those contract agreements are approved to go over budget by either $500,000 or 10 percent more than the original price.

The council would have to be notified within seven business days and would make those overruns public to try to prevent future bungles like CityTime, the city’s electronic payroll system that ran almost $700 million over budget and was rife with fraud.

In May, 11 people were charged in the scam, which involved contractors and consultants accused of ripping off city funds meant for the project.

“The idea is to get ongoing information so you see earlier when a contract is blowing the budget, so then we correctively . . . decide, ‘OK, we understand why that happened. It’s unavoidable,’ or maybe say, ‘No, this project isn’t worth that much money,’ ” Quinn said of the bill.

She said highlighting cost overruns early could force agencies to do more to prevent costs from piling up before the city is on the hook for the bill.